Landau equation for very soft and Coulomb potentials near Maxwellians
Carrapatoso, Kleber; Mischler, Stéphane (2017), Landau equation for very soft and Coulomb potentials near Maxwellians, Annals of PDE, 3, 1. 10.1007/s40818-017-0021-0
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01237530
Journal nameAnnals of PDE
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Abstract (EN)This work deals with the Landau equation for very soft and Coulomb potentials near the associated Maxwellian equilibrium. We first investigate the corresponding linearized operator and develop a method to prove stability estimates of its associated semigroup in large functional spaces. We then deduce existence, uniqueness and fast decay of the solutions to the nonlinear equation in a close-to-equilibrium framework. Our result drastically improves the set of initial data compared to the one considered by Guo and Strain who established similar results in [21, 37, 38]. Our functional framework is compatible with the non perturbative frameworks developed by Villani, Desvillettes and co-authors [42, 17, 16, 13], and our main result then makes possible to improve the speed of convergence to the equilibrium established therein.
Subjects / KeywordsLandau equation, existence; uniqueness; stability; semigroup stability; very soft potentials; Coulomb potential; convergence to equilibrium
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